Why the Null Hypothesis is Not Accepted (1 of 5)

A null hypothesis is not accepted just because it
is not rejected. Data not sufficient to show convincingly that a difference
between means is not zero do not prove that the difference is zero. Such data
may even suggest that the null hypothesis is false but not be strong
enough to make a convincing case that the null hypothesis is false.
For example, if the probability value were
0.15, then one would not be ready to present one's case that the null
hypothesis is false to the (properly) skeptical scientific community.
More convincing data would be needed to do that. However, there would
be no basis to conclude that the null hypothesis is true. It may or
may not be true, there just is not strong enough evidence to reject
it. Not even in cases where there is no evidence that the null
hypothesis is false is it valid to conclude the null hypothesis is
true. If the null hypothesis is that µ1 -
µ2 is zero then the hypothesis is that the difference
is exactly zero. No experiment can distinguish between the case of no
difference between means and an extremely small difference between
means. If data are consistent with the null hypothesis, they are also
consistent with other similar hypotheses.